Order of addition

If we are adding two force vectors, F + G, is it valid to assume as in
ordinary algebra that F + G is the same as G + F?

To tell if this algebra rule also applies to vectors, we simply translate
the vector notation into ordinary algebra notation. In terms of ordinary
numbers, the components of the vector F+G would be Fx +Gx , Fy +Gy ,
and Fz + Gz , which are certainly the same three numbers as Gx + Fx ,
Gy + Fy , and Gz + Fz . Yes, F + G is the same as G + F.